Estimating Reproductive Costs with Multi-State Mark-Recapture Models, Multiple Observable States, and Temporary Emigration

Multi-state mark-recapture models have seen increased use in recent years for studies of reproductive costs. When individuals in both breeding and non-breeding states can be observed, multi-state models can be used to directly estimate reproductive costs by comparing state-specific estimates of survival and breeding probabilities. The method assumes that each state that an animal occupies is observable, an assumption that is violated if some animals are absent for one or more breeding seasons and are thus, unobservable due to temporary emigration. Previous research on the case of a single observable state and a single unobservable state has shown that non-random (Markovian) temporary emigration can, if not accounted for, bias estimates of survival. Here, simulation is used to study effects of non-random (Markovian) temporary emigration on estimates of survival and breeding probabilities for the case of two observable states and one unobservable state. Results clearly show that temporary emigration can cause estimates of survival and breeding probability to be biased if the unobservable state is ignored. Bias was either positive or negative depending on circumstances, and was sometimes severe (percent relative bias was as high as 67% for estimates of breeding probability). Accordingly, the strengths and limitations of including an unobservable state in analyses are also considered. For some situations, simply including an unobservable state will be an adequate solution. But, for those studies particularly interested in temporal variation in costs of reproduction, it will be necessary to collect other information to avoid problems of parameter constraints. Additional information can consist of data from sub-sampling during primary sampling occasions, radio telemetry, or ring recoveries.